{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using the GrainSizeTools script through JupyterLab or the notebook: first steps\n",
    "\n",
    "> IMPORTANT NOTE: This Jupyter notebook example only applies to GrainSizeTools v3.0+ Please check your script version before using this notebook. You will be able to reproduce all the results shown in this tutorial using the dataset provided with the script, the ```file data_set.txt```\n",
    "\n",
    "## Running the script in Jupyter lab/notebooks\n",
    "\n",
    "The first step is to execute the code to get all the functionalities. JupyterLab (or Jupyter notebooks) allows you to run any code using the following code snippet: ``%run + the Python file to run``. In this case you must set the full filepath that indicates where the file ``GrainSizeTools_script.py`` is located in your system. If the script was executed correctly you will see that all GrainSizeTools (GST) modules have been loaded correctly and a welcome message as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "module plot imported\nmodule averages imported\nmodule stereology imported\nmodule piezometers imported\nmodule template imported\n\n======================================================================================\nWelcome to GrainSizeTools script\n======================================================================================\nA free open-source cross-platform script to visualize and characterize grain size\npopulation and estimate differential stress via paleopizometers.\n\nVersion: v3.0.2 (2020-12-30)\nDocumentation: https://marcoalopez.github.io/GrainSizeTools/\n\nType get.functions_list() to get a list of the main methods\n\n"
     ]
    }
   ],
   "source": [
    "%run C:/Users/marco/Documents/GitHub/GrainSizeTools/grain_size_tools/GrainSizeTools_script.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Get information on the GrainSizeTools methods\n",
    "\n",
    "First, to get a list of the main methods type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\n======================================================================================\nList of main functions\n======================================================================================\nsummarize              -> get the properties of the data population\nconf_interval          -> estimate a robust confidence interval using the t-distribution\ncalc_diffstress        -> estimate diff. stress from grain size using piezometers\n\nplot.distribution      -> visualize the distribution of grain sizes and locate the averages\nplot.qq_plot           -> test the lognormality of the dataset (q-q plot + Shapiro-Wilk test)\nplot.area_weighted     -> visualize the area-weighed distribution of grain sizes\nplot.normalized        -> visualize a normalized distribution of grain sizes\n\nstereology.Saltykov    -> approximate the actual grain size distribution via the Saltykov method\nstereology.calc_shape  -> approximate the lognormal shape of the actual distribution\n======================================================================================\n\nYou can get more information about the methods using the following ways:\n    (1) Typing ? or ?? after the function name, e.g. ?summarize\n    (2) Typing help plus the name of the function, e.g. help(summarize)\n    (3) In the Spyder IDE by writing the name of the function and clicking Ctrl + I\n    (4) In Jupyter lab/notebook by enabling the \"Show contextual help\", the info\n    will pop up as soon as you write the name of the function.\n\n"
     ]
    }
   ],
   "source": [
    "get.functions_list()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The script is implemented around several modules. To access a method within a module you will have to type the name of the module and then, separated by a dot, the name of the method.For example to access the method ``qq_plot`` of the plot module you should write\n",
    "\n",
    "```python\n",
    "plot.qq_plot()\n",
    "```\n",
    "and then provide the required parameters within the parenthesis.\n",
    "\n",
    "To access the methods within a module, type the module name plus the dot and hit the tab key and a complete list of methods will pop up.\n",
    "\n",
    "### Get detailed information on methods\n",
    "\n",
    "You can get detailed information about any method or function of the script in different ways. The first is through the console using the character ? before the method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "\u001b[1;31mSignature:\u001b[0m \u001b[0mconf_interval\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mconfidence\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0.95\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mDocstring:\u001b[0m\n",
      "Estimate the confidence interval using the t-distribution with n-1\n",
      "degrees of freedom t(n-1). This is the way to go when sample size is\n",
      "small (n < 30) and the standard deviation cannot be estimated accurately.\n",
      "For large datasets, the t-distribution approaches the normal distribution.\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "data : array-like\n",
      "    the dataset\n",
      "\n",
      "confidence : float between 0 and 1, optional\n",
      "    the confidence interval, default = 0.95\n",
      "\n",
      "Assumptions\n",
      "-----------\n",
      "the data follows a normal or symmetric distrubution (when sample size\n",
      "is large)\n",
      "\n",
      "call_function(s)\n",
      "----------------\n",
      "Scipy's t.interval\n",
      "\n",
      "Returns\n",
      "-------\n",
      "the arithmetic mean, the error, and the limits of the confidence interval\n",
      "\u001b[1;31mFile:\u001b[0m      c:\\users\\marco\\documents\\github\\grainsizetools\\grain_size_tools\\grainsizetools_script.py\n",
      "\u001b[1;31mType:\u001b[0m      function\n"
     ],
     "name": "stdout"
    }
   ],
   "source": [
    "?conf_interval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another option in Jupyter's lab is to get the information interactively without having to call it from the console. To do this, right-click on the mouse and select \"Show Context Help\" from the menu. Now, every time you write a method in the interactive console, all the information will automatically appear in the \"Contextual help\" window. In this case, you may prefer to rearrange the windows using drag and drop so that you can see the notebook and the contextual help in parallel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# Importing tabular data\n",
    "\n",
    "For this, [Pandas](https://pandas.pydata.org/about/index.html) is the de facto standard Python library for data analysis and manipulation of table-like datasets (CSV, excel or text files among others). The library includes several tools for reading files and handling of missing data and when running the GrainSizeTools script pandas is imported as ```pd``` for its general use.\n",
    "\n",
    "All Pandas methods to read data are all named ```pd.read_*``` where * is the file type. For example:\n",
    "\n",
    "```python\n",
    "pd.read_csv()      # read csv or txt files, default delimiter is ','\n",
    "pd.read_table()    # read general delimited file, default delimiter is '\\t' (TAB)\n",
    "pd.read_excel()    # read excel files\n",
    "pd.read_html()     # read HTML tables\n",
    "# etc.\n",
    "```\n",
    "For other supported file types see https://pandas.pydata.org/pandas-docs/stable/user_guide/io.html\n",
    "\n",
    "The only mandatory argument for the reading methods is to define the path (local or URL) with the location of the file to be imported as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "               Area  Circ.    Feret  FeretX  FeretY  FeretAngle  MinFeret  \\\n",
       "0        1   157.25  0.680   18.062  1535.0     0.5     131.634    13.500   \n",
       "1        2  2059.75  0.771   62.097   753.5    16.5     165.069    46.697   \n",
       "2        3  1961.50  0.842   57.871   727.0    65.0      71.878    46.923   \n",
       "3        4  5428.50  0.709  114.657  1494.5    83.5      19.620    63.449   \n",
       "4        5   374.00  0.699   29.262  2328.0    34.0      33.147    16.000   \n",
       "...    ...      ...    ...      ...     ...     ...         ...       ...   \n",
       "2656  2657   452.50  0.789   28.504  1368.0  1565.5     127.875    22.500   \n",
       "2657  2658  1081.25  0.756   47.909  1349.5  1569.5     108.246    31.363   \n",
       "2658  2659   513.50  0.720   32.962  1373.0  1586.0     112.286    20.496   \n",
       "2659  2660   277.75  0.627   29.436  1316.0  1601.5     159.102    17.002   \n",
       "2660  2661   725.00  0.748   39.437  1335.5  1615.5     129.341    28.025   \n",
       "\n",
       "         AR  Round  Solidity  \n",
       "0     1.101  0.908     0.937  \n",
       "1     1.314  0.761     0.972  \n",
       "2     1.139  0.878     0.972  \n",
       "3     1.896  0.528     0.947  \n",
       "4     1.515  0.660     0.970  \n",
       "...     ...    ...       ...  \n",
       "2656  1.235  0.810     0.960  \n",
       "2657  1.446  0.692     0.960  \n",
       "2658  1.493  0.670     0.953  \n",
       "2659  1.727  0.579     0.920  \n",
       "2660  1.351  0.740     0.960  \n",
       "\n",
       "[2661 rows x 11 columns]"
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th></th>\n      <th>Area</th>\n      <th>Circ.</th>\n      <th>Feret</th>\n      <th>FeretX</th>\n      <th>FeretY</th>\n      <th>FeretAngle</th>\n      <th>MinFeret</th>\n      <th>AR</th>\n      <th>Round</th>\n      <th>Solidity</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>157.25</td>\n      <td>0.680</td>\n      <td>18.062</td>\n      <td>1535.0</td>\n      <td>0.5</td>\n      <td>131.634</td>\n      <td>13.500</td>\n      <td>1.101</td>\n      <td>0.908</td>\n      <td>0.937</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2</td>\n      <td>2059.75</td>\n      <td>0.771</td>\n      <td>62.097</td>\n      <td>753.5</td>\n      <td>16.5</td>\n      <td>165.069</td>\n      <td>46.697</td>\n      <td>1.314</td>\n      <td>0.761</td>\n      <td>0.972</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>3</td>\n      <td>1961.50</td>\n      <td>0.842</td>\n      <td>57.871</td>\n      <td>727.0</td>\n      <td>65.0</td>\n      <td>71.878</td>\n      <td>46.923</td>\n      <td>1.139</td>\n      <td>0.878</td>\n      <td>0.972</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4</td>\n      <td>5428.50</td>\n      <td>0.709</td>\n      <td>114.657</td>\n      <td>1494.5</td>\n      <td>83.5</td>\n      <td>19.620</td>\n      <td>63.449</td>\n      <td>1.896</td>\n      <td>0.528</td>\n      <td>0.947</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>5</td>\n      <td>374.00</td>\n      <td>0.699</td>\n      <td>29.262</td>\n      <td>2328.0</td>\n      <td>34.0</td>\n      <td>33.147</td>\n      <td>16.000</td>\n      <td>1.515</td>\n      <td>0.660</td>\n      <td>0.970</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>2656</th>\n      <td>2657</td>\n      <td>452.50</td>\n      <td>0.789</td>\n      <td>28.504</td>\n      <td>1368.0</td>\n      <td>1565.5</td>\n      <td>127.875</td>\n      <td>22.500</td>\n      <td>1.235</td>\n      <td>0.810</td>\n      <td>0.960</td>\n    </tr>\n    <tr>\n      <th>2657</th>\n      <td>2658</td>\n      <td>1081.25</td>\n      <td>0.756</td>\n      <td>47.909</td>\n      <td>1349.5</td>\n      <td>1569.5</td>\n      <td>108.246</td>\n      <td>31.363</td>\n      <td>1.446</td>\n      <td>0.692</td>\n      <td>0.960</td>\n    </tr>\n    <tr>\n      <th>2658</th>\n      <td>2659</td>\n      <td>513.50</td>\n      <td>0.720</td>\n      <td>32.962</td>\n      <td>1373.0</td>\n      <td>1586.0</td>\n      <td>112.286</td>\n      <td>20.496</td>\n      <td>1.493</td>\n      <td>0.670</td>\n      <td>0.953</td>\n    </tr>\n    <tr>\n      <th>2659</th>\n      <td>2660</td>\n      <td>277.75</td>\n      <td>0.627</td>\n      <td>29.436</td>\n      <td>1316.0</td>\n      <td>1601.5</td>\n      <td>159.102</td>\n      <td>17.002</td>\n      <td>1.727</td>\n      <td>0.579</td>\n      <td>0.920</td>\n    </tr>\n    <tr>\n      <th>2660</th>\n      <td>2661</td>\n      <td>725.00</td>\n      <td>0.748</td>\n      <td>39.437</td>\n      <td>1335.5</td>\n      <td>1615.5</td>\n      <td>129.341</td>\n      <td>28.025</td>\n      <td>1.351</td>\n      <td>0.740</td>\n      <td>0.960</td>\n    </tr>\n  </tbody>\n</table>\n<p>2661 rows × 11 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "# set the filepath, note that is enclosed in quotation marks\n",
    "filepath = 'C:/Users/marco/Documents/GitHub/GrainSizeTools/grain_size_tools/DATA/data_set.txt'\n",
    "\n",
    "# import the data\n",
    "dataset = pd.read_table(filepath)\n",
    "\n",
    "#display the data\n",
    "dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some important things to note about the code snippet used above are:\n",
    "\n",
    "- We used the ``pd.read_table()`` method to import the file. By default, this method assumes that the data to import is stored in a text file separated by tabs. Alternatively you can use the ``pd.read_csv()`` method (note that csv means comma-separated values) and set the delimiter to ``'\\t'`` as follows: ``pd.read_csv(filepath, sep='\\t')``.\n",
    "- When calling the variable ``dataset`` it returs a visualization of the dataset imported, which is a tabular-like dataset with 2661 entries and 11 columns with different grain properties.\n",
    "\n",
    "In Python, this type of tabular-like objects are called (Pandas) *DataFrame* and allow a flexible and easy to use data analysis. Just for checking:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "pandas.core.frame.DataFrame"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "# show the variable type\n",
    "type(dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> 👉 Pandas' reading methods give you a lot of control over how a file is read. To keep things simple, I list the most commonly used arguments:\n",
    "\n",
    "```python\n",
    "sep         # Delimiter/separator to use.\n",
    "header      # Row number(s) to use as the column names. By default it takes the first row as the column names (header=0). If there is no columns names in the file you must set header=None\n",
    "skiprows    # Number of lines to skip at the start of the file (an integer).\n",
    "na_filter   # Detect missing value markers. False by default.\n",
    "sheet_name  # Only excel files, the excel sheet name either a number or the full name.\n",
    "```\n",
    "\n",
    "> more details on Pandas csv read method: https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.read_csv.html\n",
    "\n",
    "The GrainSizeTools script includes a method named ```get_filepath()``` to get the path of a file through a file selection dialog instead of directly writing it. This can be used in two ways:\n",
    "\n",
    "```python\n",
    "# store the path in a variable (here named filepath for convenience) and then use it when calling the read method\n",
    "filepath = get_filepath()\n",
    "dataset = pd.read_csv(filepath, sep='\\t')\n",
    "\n",
    "# use get_filepath() directly within the read method\n",
    "dataset = pd.read_csv(get_filepath(), sep='\\t')\n",
    "```\n",
    "\n",
    "Lastly, Pandas also allows to directly import tabular data from the clipboard (i.e. data copied using copy-paste commands). For example, after copying the table from a text file, excel spreadsheet or a website using: \n",
    "\n",
    "```python\n",
    "dataset = pd.read_clipboard()\n",
    "```\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic data manipulation (using Pandas)\n",
    "\n",
    "Let's first see how the data set looks like. Instead of calling the variable (as in the example before) we now use the ``head()`` and ``tail()`` methods so that it only shows us the first (or last) rows of the data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "         Area  Circ.    Feret  FeretX  FeretY  FeretAngle  MinFeret     AR  \\\n",
       "0  1   157.25  0.680   18.062  1535.0     0.5     131.634    13.500  1.101   \n",
       "1  2  2059.75  0.771   62.097   753.5    16.5     165.069    46.697  1.314   \n",
       "2  3  1961.50  0.842   57.871   727.0    65.0      71.878    46.923  1.139   \n",
       "3  4  5428.50  0.709  114.657  1494.5    83.5      19.620    63.449  1.896   \n",
       "4  5   374.00  0.699   29.262  2328.0    34.0      33.147    16.000  1.515   \n",
       "\n",
       "   Round  Solidity  \n",
       "0  0.908     0.937  \n",
       "1  0.761     0.972  \n",
       "2  0.878     0.972  \n",
       "3  0.528     0.947  \n",
       "4  0.660     0.970  "
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th></th>\n      <th>Area</th>\n      <th>Circ.</th>\n      <th>Feret</th>\n      <th>FeretX</th>\n      <th>FeretY</th>\n      <th>FeretAngle</th>\n      <th>MinFeret</th>\n      <th>AR</th>\n      <th>Round</th>\n      <th>Solidity</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1</td>\n      <td>157.25</td>\n      <td>0.680</td>\n      <td>18.062</td>\n      <td>1535.0</td>\n      <td>0.5</td>\n      <td>131.634</td>\n      <td>13.500</td>\n      <td>1.101</td>\n      <td>0.908</td>\n      <td>0.937</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2</td>\n      <td>2059.75</td>\n      <td>0.771</td>\n      <td>62.097</td>\n      <td>753.5</td>\n      <td>16.5</td>\n      <td>165.069</td>\n      <td>46.697</td>\n      <td>1.314</td>\n      <td>0.761</td>\n      <td>0.972</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>3</td>\n      <td>1961.50</td>\n      <td>0.842</td>\n      <td>57.871</td>\n      <td>727.0</td>\n      <td>65.0</td>\n      <td>71.878</td>\n      <td>46.923</td>\n      <td>1.139</td>\n      <td>0.878</td>\n      <td>0.972</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4</td>\n      <td>5428.50</td>\n      <td>0.709</td>\n      <td>114.657</td>\n      <td>1494.5</td>\n      <td>83.5</td>\n      <td>19.620</td>\n      <td>63.449</td>\n      <td>1.896</td>\n      <td>0.528</td>\n      <td>0.947</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>5</td>\n      <td>374.00</td>\n      <td>0.699</td>\n      <td>29.262</td>\n      <td>2328.0</td>\n      <td>34.0</td>\n      <td>33.147</td>\n      <td>16.000</td>\n      <td>1.515</td>\n      <td>0.660</td>\n      <td>0.970</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "dataset.head()  # returns 5 rows by default, you can define any number within the parenthesis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The example dataset has 11 different columns (one without a name). To interact with one of the columns we must call its name in square brackets with the name in quotes as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0         314.5\n",
       "1        4119.5\n",
       "2        3923.0\n",
       "3       10857.0\n",
       "4         748.0\n",
       "         ...   \n",
       "2656      905.0\n",
       "2657     2162.5\n",
       "2658     1027.0\n",
       "2659      555.5\n",
       "2660     1450.0\n",
       "Name: Area, Length: 2661, dtype: float64"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "# get the column 'Area' and multiplied by two\n",
    "dataset['Area'] * 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to remove one or more columns, you can do it with the ``drop()`` method. For example, let's remove the column without a name."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "      Area  Circ.   Feret  FeretX  FeretY  FeretAngle  MinFeret     AR  Round  \\\n",
       "0   157.25  0.680  18.062  1535.0     0.5     131.634    13.500  1.101  0.908   \n",
       "1  2059.75  0.771  62.097   753.5    16.5     165.069    46.697  1.314  0.761   \n",
       "2  1961.50  0.842  57.871   727.0    65.0      71.878    46.923  1.139  0.878   \n",
       "\n",
       "   Solidity  \n",
       "0     0.937  \n",
       "1     0.972  \n",
       "2     0.972  "
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Area</th>\n      <th>Circ.</th>\n      <th>Feret</th>\n      <th>FeretX</th>\n      <th>FeretY</th>\n      <th>FeretAngle</th>\n      <th>MinFeret</th>\n      <th>AR</th>\n      <th>Round</th>\n      <th>Solidity</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>157.25</td>\n      <td>0.680</td>\n      <td>18.062</td>\n      <td>1535.0</td>\n      <td>0.5</td>\n      <td>131.634</td>\n      <td>13.500</td>\n      <td>1.101</td>\n      <td>0.908</td>\n      <td>0.937</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2059.75</td>\n      <td>0.771</td>\n      <td>62.097</td>\n      <td>753.5</td>\n      <td>16.5</td>\n      <td>165.069</td>\n      <td>46.697</td>\n      <td>1.314</td>\n      <td>0.761</td>\n      <td>0.972</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1961.50</td>\n      <td>0.842</td>\n      <td>57.871</td>\n      <td>727.0</td>\n      <td>65.0</td>\n      <td>71.878</td>\n      <td>46.923</td>\n      <td>1.139</td>\n      <td>0.878</td>\n      <td>0.972</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "# Remove the column without a name from the DataFrame\n",
    "dataset.drop(columns=' ', inplace=True)\n",
    "dataset.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "      Area  Circ.   Feret  FeretAngle  MinFeret     AR  Round  Solidity\n",
       "0   157.25  0.680  18.062     131.634    13.500  1.101  0.908     0.937\n",
       "1  2059.75  0.771  62.097     165.069    46.697  1.314  0.761     0.972\n",
       "2  1961.50  0.842  57.871      71.878    46.923  1.139  0.878     0.972"
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Area</th>\n      <th>Circ.</th>\n      <th>Feret</th>\n      <th>FeretAngle</th>\n      <th>MinFeret</th>\n      <th>AR</th>\n      <th>Round</th>\n      <th>Solidity</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>157.25</td>\n      <td>0.680</td>\n      <td>18.062</td>\n      <td>131.634</td>\n      <td>13.500</td>\n      <td>1.101</td>\n      <td>0.908</td>\n      <td>0.937</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2059.75</td>\n      <td>0.771</td>\n      <td>62.097</td>\n      <td>165.069</td>\n      <td>46.697</td>\n      <td>1.314</td>\n      <td>0.761</td>\n      <td>0.972</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1961.50</td>\n      <td>0.842</td>\n      <td>57.871</td>\n      <td>71.878</td>\n      <td>46.923</td>\n      <td>1.139</td>\n      <td>0.878</td>\n      <td>0.972</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "# If you want to remove more than one column pass a list of columns\n",
    "dataset.drop(columns=['FeretX', 'FeretY'], inplace=True)\n",
    "dataset.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create new columns\n",
    "\n",
    "The example dataset does not contain any column with the grain diameters and therefore we have to estimate them. For example, assuming the data comes from a thin section, you can estimate the apparent diameters from the section areas using the equivalent circular diameter (ECD) formula which is\n",
    "\n",
    "$ECD = 2 \\cdot \\sqrt{areas / \\pi}$\n",
    "\n",
    "we will call the new column ``'diameters'``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "      Area  Circ.    Feret  FeretAngle  MinFeret     AR  Round  Solidity  \\\n",
       "0   157.25  0.680   18.062     131.634    13.500  1.101  0.908     0.937   \n",
       "1  2059.75  0.771   62.097     165.069    46.697  1.314  0.761     0.972   \n",
       "2  1961.50  0.842   57.871      71.878    46.923  1.139  0.878     0.972   \n",
       "3  5428.50  0.709  114.657      19.620    63.449  1.896  0.528     0.947   \n",
       "4   374.00  0.699   29.262      33.147    16.000  1.515  0.660     0.970   \n",
       "\n",
       "   diameters  \n",
       "0  14.149803  \n",
       "1  51.210889  \n",
       "2  49.974587  \n",
       "3  83.137121  \n",
       "4  21.821815  "
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Area</th>\n      <th>Circ.</th>\n      <th>Feret</th>\n      <th>FeretAngle</th>\n      <th>MinFeret</th>\n      <th>AR</th>\n      <th>Round</th>\n      <th>Solidity</th>\n      <th>diameters</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>157.25</td>\n      <td>0.680</td>\n      <td>18.062</td>\n      <td>131.634</td>\n      <td>13.500</td>\n      <td>1.101</td>\n      <td>0.908</td>\n      <td>0.937</td>\n      <td>14.149803</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>2059.75</td>\n      <td>0.771</td>\n      <td>62.097</td>\n      <td>165.069</td>\n      <td>46.697</td>\n      <td>1.314</td>\n      <td>0.761</td>\n      <td>0.972</td>\n      <td>51.210889</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1961.50</td>\n      <td>0.842</td>\n      <td>57.871</td>\n      <td>71.878</td>\n      <td>46.923</td>\n      <td>1.139</td>\n      <td>0.878</td>\n      <td>0.972</td>\n      <td>49.974587</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>5428.50</td>\n      <td>0.709</td>\n      <td>114.657</td>\n      <td>19.620</td>\n      <td>63.449</td>\n      <td>1.896</td>\n      <td>0.528</td>\n      <td>0.947</td>\n      <td>83.137121</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>374.00</td>\n      <td>0.699</td>\n      <td>29.262</td>\n      <td>33.147</td>\n      <td>16.000</td>\n      <td>1.515</td>\n      <td>0.660</td>\n      <td>0.970</td>\n      <td>21.821815</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "dataset['diameters'] = 2 * np.sqrt(dataset['Area'] / np.pi)\n",
    "dataset.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see a new column named diameters.\n",
    "\n",
    "> 👉  In the examples above we define the square root as ``np.sqrt``, the arithmetic mean as ``np.mean``, and pi as  ``np.pi``. In this case, ``np.`` stems for NumPy or numerical Python, a core package for scientific computing with Python, and the keyword after the dot is the method or the scientific value to be applied. If you write in the console ``np.`` and then press the TAB key, you will see a large list of available methods. In general, the method names are equivalent to those used in MATLAB or R but always by adding the ``np.`` first.\n",
    "\n",
    "### A list of useful Pandas methods\n",
    "\n",
    "Some things you might want to try (just copy-paste in interactive cells below and explore):\n",
    "\n",
    "```python\n",
    "# Reduction\n",
    "dataset.mean()          # estimate the mean for all columns\n",
    "dataset['Area'].mean()  # estimate the mean only for the column Area\n",
    "dataset.std()           # estimate the (Bessel corrected) standard deviation\n",
    "dataset.median()        # estimate the median\n",
    "dataset.mad()           # estimate the mean absolute deviation\n",
    "dataset.var()           # estimate the unbiased variace\n",
    "dataset.sem()           # estimate the standard error of the mean\n",
    "dataset.skew()          # estimate the sample skewness\n",
    "dataset.kurt()          # estimate the sample kurtosis\n",
    "dataset.quantile()      # estimate the sample quantile\n",
    "\n",
    "# Information\n",
    "dataset.describe()   # generate descriptive statistics\n",
    "dataset.info()       # display info of the DataFrame\n",
    "dataset.shape()      # (rows, columns)\n",
    "dataset.count()      # number of non-null values\n",
    "\n",
    "dataset.dropna()        # remove missing values from the data\n",
    "\n",
    "# writing to disk\n",
    "dataset.to_csv(filename)    # save as csv file, the filename must be within quotes\n",
    "dataset.to_excel(filename)  # save as excel file\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Area          1213.823750\n",
       "Circ.            0.730233\n",
       "Feret           44.808749\n",
       "FeretAngle      90.622313\n",
       "MinFeret        31.016330\n",
       "AR               1.451459\n",
       "Round            0.719253\n",
       "Solidity         0.943795\n",
       "diameters       34.785694\n",
       "dtype: float64"
      ]
     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "# estimate the mean of all columns\n",
    "dataset.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "               Area        Circ.        Feret   FeretAngle     MinFeret  \\\n",
       "count   2661.000000  2661.000000  2661.000000  2661.000000  2661.000000   \n",
       "mean    1213.823750     0.730233    44.808749    90.622313    31.016330   \n",
       "std     1331.462328     0.069441    21.764062    53.570466    17.079455   \n",
       "min        8.000000     0.377000     4.301000     1.071000     2.500000   \n",
       "25%      346.500000     0.691000    29.108000    41.566000    18.063000   \n",
       "50%      780.750000     0.742000    41.404000    87.274000    28.306000   \n",
       "75%     1589.500000     0.780000    56.447000   141.746000    40.791000   \n",
       "max    19259.750000     0.873000   177.229000   179.576000   146.363000   \n",
       "\n",
       "                AR        Round     Solidity    diameters  \n",
       "count  2661.000000  2661.000000  2661.000000  2661.000000  \n",
       "mean      1.451459     0.719253     0.943795    34.785694  \n",
       "std       0.337358     0.136751     0.027590    18.318569  \n",
       "min       1.004000     0.236000     0.764000     3.191538  \n",
       "25%       1.211000     0.626000     0.932000    21.004226  \n",
       "50%       1.368000     0.731000     0.950000    31.529062  \n",
       "75%       1.597000     0.826000     0.963000    44.986823  \n",
       "max       4.244000     0.996000     0.985000   156.595898  "
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Area</th>\n      <th>Circ.</th>\n      <th>Feret</th>\n      <th>FeretAngle</th>\n      <th>MinFeret</th>\n      <th>AR</th>\n      <th>Round</th>\n      <th>Solidity</th>\n      <th>diameters</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n      <td>2661.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td>1213.823750</td>\n      <td>0.730233</td>\n      <td>44.808749</td>\n      <td>90.622313</td>\n      <td>31.016330</td>\n      <td>1.451459</td>\n      <td>0.719253</td>\n      <td>0.943795</td>\n      <td>34.785694</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>1331.462328</td>\n      <td>0.069441</td>\n      <td>21.764062</td>\n      <td>53.570466</td>\n      <td>17.079455</td>\n      <td>0.337358</td>\n      <td>0.136751</td>\n      <td>0.027590</td>\n      <td>18.318569</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>8.000000</td>\n      <td>0.377000</td>\n      <td>4.301000</td>\n      <td>1.071000</td>\n      <td>2.500000</td>\n      <td>1.004000</td>\n      <td>0.236000</td>\n      <td>0.764000</td>\n      <td>3.191538</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>346.500000</td>\n      <td>0.691000</td>\n      <td>29.108000</td>\n      <td>41.566000</td>\n      <td>18.063000</td>\n      <td>1.211000</td>\n      <td>0.626000</td>\n      <td>0.932000</td>\n      <td>21.004226</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td>780.750000</td>\n      <td>0.742000</td>\n      <td>41.404000</td>\n      <td>87.274000</td>\n      <td>28.306000</td>\n      <td>1.368000</td>\n      <td>0.731000</td>\n      <td>0.950000</td>\n      <td>31.529062</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td>1589.500000</td>\n      <td>0.780000</td>\n      <td>56.447000</td>\n      <td>141.746000</td>\n      <td>40.791000</td>\n      <td>1.597000</td>\n      <td>0.826000</td>\n      <td>0.963000</td>\n      <td>44.986823</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td>19259.750000</td>\n      <td>0.873000</td>\n      <td>177.229000</td>\n      <td>179.576000</td>\n      <td>146.363000</td>\n      <td>4.244000</td>\n      <td>0.996000</td>\n      <td>0.985000</td>\n      <td>156.595898</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "# Generate descriptive statistics\n",
    "dataset.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "metadata": {},
     "execution_count": 13
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "dataset[['Circ.', 'Round', 'Solidity']].boxplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}